It's misleading because saying "search the computer" implies a breadth of scan that isn't present. That's like saying a website "searches the computer" to grab cookies generated by that site; technically true but worded to be misleading.

To be clear this is bad, but it's important to be clear when explaining why it is bad to avoid creating resentment when the person you are explaining it to looks deeper into it themself and finds that it's not as bad as your explanation was implying.

I believe the point they’re trying to make is that they have access to APIs which describe particular software on your PC. You can argue based on the fact that, yes, the software is persisted on your filesystem. However, the API they access brokers [meta]data about the software. It’s not a filesystem API. If I add arbitrary files to an extension directory under my browsers path for extension persistence, they probably cannot see those arbitrary files unless the extension is built to allow it.

There is a big difference between having direct and broad read access to the filesystem, versus the much smaller volume of data they can infer about your filesystem using APIs for browser extension data.